Finite Group Databasebeta

← #35303886

Subgroups — #35303886

Order 21248.

406 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128051C211yesmaximal, characteristic
2#24907634C211yesmaximal, characteristic
3#24906149C211yesmaximal, characteristic
4#24906143C211yesmaximal, characteristic
5#24906135C211yesmaximal, characteristic
6#24905756C211yesmaximal, characteristic
7C83×#1546C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9#19128051—21no—
10#19128051—21no—
11#19128051C414yes—
12#19127754C2211yescharacteristic
13C2×#14581727—22no—
14#19127725C2211yescharacteristic
15C2×#14581716—22no—
16C2×C4×C83⋊C8C2211yescharacteristic
17#19127449—22no—
18#19127447—22no—
19#19127446—22no—
20#19127423—21no—
21#19127422—21no—
22C2×C4⋊Q8×C83C2211yescharacteristic
23#431×C83C2211yescharacteristic
24#423×C83C2211yescharacteristic
25#332×C83—22no—
26C22×Dic166—21no—
27C2×#13050574—21no—
28C22×C83⋊C8D412yes—
29#14581792—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792C2×C412yes—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35#14581727—44no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)D412yes—
39#14581716—24no—
40#14581716—24no—
41C22⋊(C83⋊C8)—21no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8C2×C412yes—
44C4×C83⋊C8D411yescharacteristic
45C4×C83⋊C8D411yescharacteristic
46C22×Q8×C83—21no—
47C2×M16×C83—21no—
48C4⋊Q8×C83—21no—
49C4⋊Q8×C83—21no—
50C4⋊Q8×C83—21no—
51C4⋊Q8×C83C2×C412yes—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C42×C83C2311yescharacteristic
55C4⋊C8×C83—21no—
56C4⋊C8×C83—21no—
57C4⋊C8×C83D412yes—
58C22⋊C8×C83—21no—
59C4×C8×C83—21no—
60C2×Dic166—22no—
61C2×Dic166—41no—
62C2×Dic166—82no—
63C22×Dic83—41no—
64#13050574—42no—
65C2×C83⋊C8—22no—
66C2×C83⋊C8—22no—
67C2×C83⋊C8—22no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8C22⋊C412yes—
70C2×C83⋊C8C22⋊C412yes—
71C4⋊Dic83—22no—
72C4⋊Dic83—22no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C2×Q8×C83—22no—
76C2×Q8×C83—41no—
77C2×Q8×C83—42no—
78C2×Q8×C83—42no—
79C22×C4×C83—41no—
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83#4111yescharacteristic
82C22×C4×C83#4111yescharacteristic
83M16×C83—42no—
84C2×C8×C83—22no—
85C2×C8×C83—41no—
86C4⋊C4×C83—22no—
87C4⋊C4×C83—22no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C42×C83C22×C411yescharacteristic
91C42×C83C2×D411yescharacteristic
92C42×C83C2×D411yescharacteristic
93C42×C83C2×D411yescharacteristic
94C23×C83#12411yescharacteristic
95Q8×C83—44no—
96Q8×C83—81no—
97Q8×C83—81no—
98C2×C4×C83—22no—
99C2×C4×C83—22no—
100C2×C4×C83—42no—
101C2×C4×C83—82no—
102C2×C4×C83C2×C22⋊C411yescharacteristic
103C2×C4×C83C4×D411yescharacteristic
104C2×C4×C83C4×D411yescharacteristic
105C2×C4×C83#12111yescharacteristic
106C2×C4×C83#12111yescharacteristic
107C2×C4×C83#12711yescharacteristic
108C2×C4×C83AGL(1,ℤ/8)12yes—
109C2×C4×C83#13712yes—
110C2×Dic83—42no—
111C2×Dic83—82no—
112Dic166—82no—
113Dic166—82no—
114C8×C83—42no—
115C8×C83—81no—
116C83⋊C8—22no—
117C83⋊C8—22no—
118C83⋊C8—42no—
119C83⋊C8—81no—
120C22×C83—21no—
121C22×C83—21no—
122C22×C83#39011yescharacteristic
123C22×C83#48912yes—
124C4×C83—21no—
125C4×C83—21no—
126C4×C83—82no—
127C4×C83#41712yes—
128C4×C83#47112yes—
129C4×C83#47312yes—
130C4×C83#49611yescharacteristic
131C4×C83#49711yescharacteristic
132Dic83—82no—
133#9775—831nomaximal, Sylow
134C2×C83—22no—
135C2×C83#195911yescharacteristic
136C2×C83#197711yescharacteristic
137C2×C83#197911yescharacteristic
138C2×#487—831no—
139#1848—831no—
140#1549—831no—
141#1548—831no—
142#1546—831no—
143#1546D8311yescharacteristic
144#1452—831no—
145C83#977511yescharacteristic, complemented, Sylow
146C2×C4⋊Q8—831no—
147C2×C4⋊Q8C2×D8311yescharacteristic
148#487—834no—
149#487—1661no—
150#487—1661no—
151#431—831no—
152#431C2×D8311yescharacteristic
153C2×#108—1662no—
154#423—831no—
155#423C2×D8311yescharacteristic
156C2×#103—1662no—
157C2×C4×C8—831no—
158#333—1662no—
159#332—22no—
160#332—1662no—
161#332—1662no—
162#322—1661no—
163#322—1661no—
164C22×Q8—21no—
165C22×Q8—1661no—
166C2×M16—21no—
167C2×M16—1661no—
168C22×C8—832no—
169C4⋊Q8—21no—
170C4⋊Q8—21no—
171C4⋊Q8—21no—
172C4⋊Q8—832no—
173C4⋊Q8—1661no—
174C4⋊Q8—1661no—
175C4⋊Q8—1661no—
176C4⋊Q8C4×D8312yes—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—1661no—
180C2×C4⋊C4—1661no—
181C2×C42C22×D8311yescharacteristic
182#108—3324no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—832no—
186C4⋊C8—1661no—
187C4⋊C8—1661no—
188C4⋊C8C22⋊D8312yes—
189#103—1664no—
190#103—1664no—
191C22⋊C8—21no—
192C22⋊C8—1661no—
193C4×C8—21no—
194C4×C8—832no—
195C4×C8—831no—
196C4×C8—831no—
197C4×C8—1661no—
198C2×Q8—22no—
199C2×Q8—41no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—3321no—
203C2×Q8—6642no—
204C2×Q8—1662no—
205C22×C4—41no—
206C22×C4—3321no—
207C22×C4D4×D8311yescharacteristic
208C22×C4#1305058911yescharacteristic
209C22×C4#1305059011yescharacteristic
210M16—42no—
211M16—3322no—
212C2×C8—22no—
213C2×C8—41no—
214C2×C8—3321no—
215C2×C8—832no—
216C2×C8—832no—
217C2×C8—1662no—
218C2×C8—1662no—
219C2×C8—1662no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—3321no—
225C4⋊C4—3321no—
226C4⋊C4—1662no—
227C4⋊C4—1662no—
228C42C2×C4×D8311yescharacteristic
229C42D4×D8311yescharacteristic
230C42D4×D8311yescharacteristic
231C42C2×C22⋊D8311yescharacteristic
232C23#1458177811yescharacteristic
233Q8—44no—
234Q8—81no—
235Q8—81no—
236Q8—6642no—
237Q8—6642no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—82no—
242C2×C4—3322no—
243C2×C4—6642no—
244C2×C4C22⋊C4×D8311yescharacteristic
245C2×C4(C22⋊D83)⋊C411yescharacteristic
246C2×C4C4×C22⋊D8311yescharacteristic
247C2×C4#1458176411yescharacteristic
248C2×C4#1458176511yescharacteristic
249C2×C4#1458178811yescharacteristic
250C2×C4#1458181612yes—
251C2×C4#1458182112yes—
252C8—42no—
253C8—81no—
254C8—3322no—
255C8—6641no—
256C8—1662no—
257C8—1662no—
258C22—21no—
259C22—21no—
260C22#1912760111yescharacteristic
261C22#1912805912yes—
262C4—21no—
263C4—21no—
264C4—82no—
265C4—6642no—
266C4#1912769912yes—
267C4#1912796712yes—
268C4#1912797412yes—
269C4#1912808911yescharacteristic
270C4#1912809211yescharacteristic
271C2—22no—
272C2#2490827811yescharacteristic
273C2#2490836711yescharacteristic
274C2#2490837711yescharacteristic
subgroupG/H
centerC22#19127601
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1546C2
socleC22×C83#390
prime radicalC23×C83#124
cosocleC2×C42×C83C23
hypercenter#1546D83
hypocenterC83#9775
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
145. C83#9775semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191280512
#249076342
#249061492
#249061432
#249061352
#249057562
C83×#15462
#977583